Bifurcation analysis of a diffusive predator-prey model with prey social behavior and predator harvesting

In this research, we investigate the influence of predator harvesting on the predator-prey interaction in the presence of prey social behavior using a reaction-diffusion system subject to the Neumann boundary conditions. It has been proved that the investigated model can undergo Hopf, Turing-Hopf bifurcation, which indicates the possibility of having a homogenous/nonhomogeneous periodic solution under some conditions on the model parameters. The stability of these periodic solutions is studied using the normal form on the center of the manifold theory. The obtained mathematical results are checked numerically.